Abstract
This letter constructs, making use of the on-shell spinor-helicity formalism, a possible ultraviolet completion of gravity following a "bottom-up" approach. The assumptions of locality, unitarity and causality i) require an infinite tower of resonances with increasing spin and quantized mass, ii) introduce a duality relation among crossed scattering channels, and iii) dress all gravitational amplitudes in the Standard Model with a form factor that closely resembles either the Veneziano or the Virasoro-Shapiro amplitude in string theory. As a consequence of unitarity, the theory predicts leading order deviations from General Relativity in the coupling of gravity to fermions that could be explained if space-time has torsion in addition to curvature.
Highlights
Prior to the Large Hadron Collider turning on, our tested theory of nature was a gauge effective field theory (EFT) with a scale v at which unitarity was lost perturbatively
Exposing the need for an UV completion of gravity by means of its similarities with the Standard Model (SM) is preeminently a particle physicist “bottom-up” approach, and it is not to say that this is the sole issue in gravity that needs addressing
One can further elaborate that the above formulation, even within particle physics and EFT, is obscured by
Summary
Prior to the Large Hadron Collider turning on, our tested theory of nature was a gauge effective field theory (EFT) with a scale v at which unitarity was lost perturbatively. Exposing the need for an UV completion of gravity by means of its similarities with the Standard Model (SM) is preeminently a particle physicist “bottom-up” approach, and it is not to say that this is the sole issue in gravity that needs addressing (open problems range from a nonperturbative formulation to the understanding of singularities relevant in cosmology and astrophysics [1]) It is, the point of view that rules the course of this paper. Positivity, derived from unitarity, will play a central role in the analysis of this paper These principles impose, in addition, stringent constraints on the high-energy behavior of scattering amplitudes [12]; of relevance in this work will be the extension of the Froissart bound [13] to a theory with a massless graviton [14] in the forward limit and the Cerulus-Martin bound [15,16] in the hard scattering region. The discussion will be restricted to weak coupling and tree level, which is to say in typical EFT language that the new resonances should lie below MPl
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